[Scip] Nonlinear problem

[Stefan Vigerske]

Hi,

> Thanks Stefan. BTW, it should be max_j(x_j p_ij) - min_j(x_j p_ij). A
> mistake on my document.
>
> Now, being a complete newbie on reformulation, can you give me some tips?

   a_i^x >= max_j(x_j p_ij) - min_j(x_j p_ij)

is equivalent to

   a_i^x >= y_i^x + z_i^x
   y_i^x >=  max_j(x_j p_ij)
   z_i^x >= -min_j(x_j p_ij)

is equivalent to

   a_i^x >= y_i^x + z_i^x
   y_i^x >=  x_j p_ij  for all j
   z_i^x >= -x_j p_ij  for all j

Stefan

>
> Regards.
> -------------------------------------------------
> Julio Rojas
> jcredberry at gmail.com
>
>
>
> On Wed, Sep 14, 2011 at 4:52 PM, Stefan Vigerske
> <stefan at math.hu-berlin.de>  wrote:
>> Hi,
>>
>> I assume that the x_i,y_i,x_j,y_j are fixed parameters.
>> If you find a linear formulation for the a_i^x, a_i^y (maybe with additional
>> binary variables), then the only nonlinearity left is
>> A = a_i^x a_i^y, which SCIP can handle.
>> You could model this with ZIMPL, for example.
>>
>> The function min_j(x_j p_ij) - max_j(x_j p_ij) seems piecewise linear and
>> concave for me. It a_i^x>= min_j(x_j p_ij) - max_j(x_j p_ij) is sufficient
>> (because equality may be assumed in an optimal solution?), then you could
>> reformulate this inequality as a set of linear constraints.
>>
>> Stefan
>>
>>> Dear all. I have to solve a problem that has a linear objective
>>> function, but some nonlinear constraints. Please, see the attached pdf
>>> in order to understand the problem. Is it possible to solve it with
>>> SCIP? Is there a way to linearize it in case SCIP is not able to solve
>>> it directly?
>>>
>>> Thanks in advance. Best regards.
>>> -------------------------------------------------
>>> Julio Rojas
>>> jcredberry at gmail.com
>>>
>>>
>>>
>>> _______________________________________________
>>> Scip mailing list
>>> Scip at zib.de
>>> http://listserv.zib.de/mailman/listinfo/scip
>>
>>
>> --
>> Stefan Vigerske
>> Humboldt University Berlin, Numerical Mathematics
>> http://www.math.hu-berlin.de/~stefan
>>
>